Histories
For every, the tuple is called the elementary history of a. It serves as an indicator function for the inclusion of a letter a in an alphabet . That is,
where
Here, denotes the empty string. The history monoid is the free monoid generated by elementary histories. It is clearly a submonoid of the product monoid . The elements of are called global histories, and the projections of a global history are called individual histories.
Read more about this topic: History Monoid
Famous quotes containing the word histories:
“All histories do shew, and wise politicians do hold it necessary that, for the well-governing of every Commonweal, it behoveth man to presuppose that all men are evil, and will declare themselves so to be when occasion is offered.”
—Sir Walter Raleigh (1552–1618)
“As soon as histories are properly told there is no more need of romances.”
—Walt Whitman (1819–1892)
“The histories of the lives and fortunes of men are full of instances of this nature,—where favorable times and lucky accidents have done for them, what wisdom or skill could not.”
—Laurence Sterne (1713–1768)